Subgroups — C₃×C₁₇×C₁₉⋊D₁₉ #49145658

Order 36822.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₇×C₁₉²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₇×C₁₉⋊D₁₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₇×C₁₉²	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₉⋊D₁₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₇×D₁₉	—	19	20	no	maximal
6	C₃×C₁₉²	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
7	C₃×C₁₇×C₁₉	D₁₉	1	20	yes	complemented
8	C₁₉⋊D₁₉	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
9	C₁₇×D₁₉	—	19	20	no	—
10	C₁₉²	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
11	C₁₇×C₁₉	C₃×D₁₉	1	20	yes	complemented
12	C₃×D₁₉	—	19	20	no	—
13	C₂×C₃×C₁₇	—	361	1	no	Hall
14	C₃×C₁₉	C₁₇×D₁₉	1	20	yes	complemented
15	C₃×C₁₇	C₁₉⋊D₁₉	1	1	yes	characteristic, direct product factor, Hall
16	D₁₉	—	19	20	no	—
17	C₂×C₁₇	—	361	1	no	Hall
18	C₁₉	C₃×C₁₇×D₁₉	1	20	yes	complemented
19	C₁₇	C₃×C₁₉⋊D₁₉	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	—	361	1	no	Hall
21	C₃	C₁₇×C₁₉⋊D₁₉	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	361	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₇	C₁₉⋊D₁₉
commutator, cosocle, hypocenter	C₁₉²	C₂×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₁₇×C₁₉²	C₂
LCS	G ▷ C₁₉²
UCS	C₁ ◁ C₃×C₁₇

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.